Work & Energy Calculator
Calculate work done (W = Fd), kinetic energy (½mv²), gravitational potential energy (mgh), and power (P = W/t). With real-world context for every result.
Work and Energy Guide
Energy Forms and Conservation
Work is energy transferred by a force acting over a distance: W = F × d × cos(θ), where θ is the angle between force and displacement. The joule (J) is the SI unit: 1 J = 1 N applied over 1 m. Conservation of energy: total mechanical energy (KE + PE) remains constant in the absence of friction. A falling ball converts PE to KE — at the midpoint, half is KE and half PE. At impact (assuming no air resistance), all PE has converted to KE.
Kinetic Energy
KE = ½mv². A 70 kg person running at 5 m/s (18 km/h): KE = ½ × 70 × 25 = 875 J. A 1,000 kg car at 30 m/s (108 km/h): KE = ½ × 1000 × 900 = 450,000 J = 450 kJ. Notice that doubling speed quadruples KE (because v is squared) — this is why road speed limits exist. At 60 mph, a car has 4× the KE of 30 mph, requiring 4× the stopping distance assuming equal braking force.
Gravitational Potential Energy
GPE = mgh, where g = 9.81 m/s² near Earth's surface. A 70 kg person climbing a 10 m staircase: GPE = 70 × 9.81 × 10 = 6,867 J ≈ 6.9 kJ ≈ 1.64 food calories. This is why stair climbing burns relatively few calories from height alone — the body is also moving forwards and working against friction. A 100 kg boulder at the top of a 100 m cliff: GPE = 100 × 9.81 × 100 = 98,100 J ≈ 98 kJ.
Power
Power is the rate of doing work: P = W/t, measured in watts (W). 1 W = 1 J/s. A 75 kg person climbing a flight of stairs (3m height) in 2 seconds: W = 75 × 9.81 × 3 = 2,207 J. Power = 2207/2 = 1,104 W ≈ 1.1 kW. Professional cyclists sustain ~400 W (FTP) and peak at 1,200–1,500 W for sprint efforts. The human body is approximately 25% efficient at converting food energy to mechanical work — the rest becomes heat.
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